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Minimal time trajectories for two-level quantum systems with two bounded controls

Author(s): Boscain, Ugo; Gronberg, Fredrik; Long, Ruixing; Rabitz, Herschel

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Abstract: In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we treat the time-optimal control problem with techniques of optimal synthesis on 2D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the initial condition. (C) 2014 AIP Publishing LLC.
Publication Date: Jun-2014
Electronic Publication Date: 25-Jun-2014
Citation: Boscain, Ugo, Gronberg, Fredrik, Long, Ruixing, Rabitz, Herschel. (2014). Minimal time trajectories for two-level quantum systems with two bounded controls. JOURNAL OF MATHEMATICAL PHYSICS, 55 (10.1063/1.4882158
DOI: doi:10.1063/1.4882158
ISSN: 0022-2488
EISSN: 1089-7658
Pages: 652106-1- 652106-26
Type of Material: Journal Article
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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